Reference issues
======================

Geometry
---------

Geometry is a compound of 2 segments with 2 nodes. The initial length of segment :math:`\mathrm{Pt}1-\mathrm{Pt}2` is :math:`0.1\mathrm{m}`.


.. image:: images/1000020100000640000001E17A196B567FB3A086.png
    :width: 3.1492in
    :height: 0.9465in


.. _RefImage_1000020100000640000001E17A196B567FB3A086.png:


A, B, C models
---------------------

Segment :math:`\mathrm{Pt}3-\mathrm{Pt}1` is modeled by a discrete K_T_D_L with ELAS behavior.

Segment :math:`\mathrm{Pt}1-\mathrm{Pt}2` is modeled by a discrete K_T_D_L with the CHOC_ENDO behavior.

A mass is assigned to :math:`\mathrm{Pt}1`.


Common material properties, A, B and C models
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The mass is :math:`15\mathrm{kg}`. The spring between :math:`\mathrm{Pt}3-\mathrm{Pt}1` has a stiffness of :math:`500\mathrm{N}/\mathrm{m}` in the x, y, and z directions.


Material properties, modeling A
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The table above gives the characteristics of the material DIS_CHOC_ENDO, assigned to the discrete :math:`\mathrm{Pt}1-\mathrm{Pt}2`, for the modeling :math:`A`.

The stiffness under discharge is constant, the damping is zero.


.. csv-table::

    "Ux
    [m]", "Strength
    [N]", "Stiffness
    [N/m]", "Damping
    [N.s/m]"
    "0.00", "0.0", "2000.0", "0.0"
    "0.20", "400.0", "2000.0", "0.0"
    "0.50", "450.0", "2000.0", "0.0"
    "0.70", "400.0", "2000.0", "0.0"
    "0.95", "375.0", "2000.0", "0.0"
    "1.30", "350.0", "2000.0", "0.0"
    "1.60", "300.0", "2000.0", "0.0"
    "20.0", "300.0", "2000.0", "0.0"


The figure below shows the behavior corresponding to the data.


.. image:: images/1000020100000CC6000006654DFAFC3B70645267.png
    :width: 5.9055in
    :height: 2.9484in


.. _RefImage_1000020100000CC6000006654DFAFC3B70645267.png:

The following commands are used to define the material:

ldepla= nu.Array ([:ref:`0.0, 2.0, 5.0, 7.0, 9.50, 13.0, 16.0, 20.0, <0.0, 2.0, 5.0, 7.0, 9.50, 13.0, 16.0, 20.0,>`]) /10.0

lforce= nu.Array ([:ref:`0.0, 4.0, 4.5, 4.0, 3.75, 3.50, 3.0, 3.0, <0.0, 4.0, 4.5, 4.0, 3.75, 3.50, 3.0, 3.0,>`]) * 100.0

# Constant stiffness

lraid= nu.Array ([:ref:`2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, <2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0,>`]) * 1000.0

# Depreciation useless in static but mandatory to give

death = nu.Array ([:ref:`0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, <0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,>`])

#

fctfx **= DEFI_FONCTION (NOM_PARA =** 'X', **ABSCISSE =** ldepla, **ORDONNEE =** lforce, **)**) **

fctrd **= DEFI_FONCTION (NOM_PARA =** 'X', **ABSCISSE =** lrepla, **ORDONNEE =** stiff, **)**) **

ctam **= DEFI_FONCTION (NOM_PARA =** 'X', **ABSCISSE =** ldepla, **ORDONNEE =** lamort, **)**) **

#

Grilleac **= DEFI_MATERIAU (**

**DIS_CHOC_ENDO** = **_F (**

**FX** = fctfx, **RIGI_NOR** **= fctrd,** AMOR_NOR **** = fctam,

**DIST_1** = 0.0, **DIST_2** ** = 0.0,

**CRIT_AMOR** **=** 'INCLUS',

**)**,

**)**


Material Properties, ModelingB
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The table above gives the characteristics of the material DIS_CHOC_ENDO, assigned to the discrete :math:`\mathrm{Pt}1-\mathrm{Pt}2`, for the modeling :math:`B`.

The discharge stiffness is variable, the damping is zero.


.. csv-table::

    "Ux
    [m]", "Strength
    [N]", "Stiffness
    [N/m]", "Damping
    [N.s/m]"
    "0.00", "0.0", "2000.0", "0.0"
    "0.20", "400.0", "2000.0", "0.0"
    "0.50", "450.0", "1800.0", "0.0"
    "0.70", "400.0", "1400.0", "0.0"
    "0.95", "375.0", "1400.0", "0.0"
    "1.30", "350.0", "1350.0", "0.0"
    "1.60", "300.0", "1330.0", "0.0"
    "20.0", "300.0", "1330.0", "0.0"


Compared to modeling :math:`A`, only the definition of stiffness changes.

# Variable stiffness

lraid= nu.Array ([:ref:`2.0, 2.0, 1.8, 1.4, 1.4, 1.35, 1.33, 1.33, <2.0, 2.0, 1.8, 1.4, 1.4, 1.35, 1.33, 1.33,>`]) * 1000.0

The figure below shows the behavior corresponding to the data.


.. image:: images/1000020100000CC6000006650D7BFD7DE8F89B72.png
    :width: 5.9055in
    :height: 2.9484in


.. _RefImage_1000020100000CC6000006650D7BFD7DE8F89B72.png:


Material properties, C modeling
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The table above gives the characteristics of the material DIS_CHOC_ENDO, assigned to the discrete :math:`\mathrm{Pt}1-\mathrm{Pt}2`, for the modeling :math:`C`.

The stiffness under discharge is variable, the damping is variable.


.. csv-table::

    "Ux
    [m]", "Strength
    [N]", "Stiffness
    [N/m]", "Damping
    [N.s/m]"
    "0.00", "0.0", "2000.0", "2.0"
    "0.20", "400.0", "2000.0", "2.0"
    "0.50", "450.0", "1800.0", "2.0"
    "0.70", "400.0", "1400.0", "1.6"
    "0.95", "375.0", "1400.0", "1.6"
    "1.30", "350.0", "1350.0", "1.4"
    "1.60", "300.0", "1330.0", "1.2"
    "20.0", "300.0", "1330.0", "1.2"


Compared to modeling :math:`B`, only the definition of depreciation changes.

# Depreciation

lamor= nu.Array ([:ref:`2.0, 2.0, 2.0, 1.6, 1.6, 1.4, 1.2, 1.2, <2.0, 2.0, 2.0, 1.6, 1.6, 1.4, 1.2, 1.2,>`])

In the material definition **CRIT_AMOR** **=** 'INCLUS'.